OFDM receivers

ABSTRACT

A method and apparatus for filtering a received Orthogonal Frequency Division Multiplexed (OFDM) signal to reduce noise. The ODFM signal includes a plurality of symbols n in the time direction, each symbol including a plurality of sub-carriers k in the frequency direction, each a-th sub-carrier of each symbol being transmitted as a pilot sub-carrier with known amplitude and phase, and each symbol having its pilot sub-carriers spaced by b sub-carriers relative to the adjacent symbol. An m-tap filter is utilized for producing a filtered version of a selected pilot sub-carrier to be used in subsequent interpolation, by inputting into respective taps of the m-tap filter, m pilot sub-carriers surrounding the selected pilot sub-carrier. The m pilot sub-carriers each satisfy a relationship between n and k, wherein the relationship defines a diagonal line in the n-k plane.

FIELD OF THE INVENTION

The invention relates to a method and apparatus for filtering a receivedOFDM (Orthogonal Frequency Division Multiplexed) signal. Particularly,but not exclusively, the invention relates to receivers for OFDMsignals, in particular mobile TV receivers.

BACKGROUND OF THE INVENTION

OFDM (Orthogonal Frequency Division Multiplexing) is a transmissionscheme used in a number of applications including digital audiobroadcasting and digital TV systems (e.g. DVB-T (Digital VideoBroadcasting—Terrestrial), DVB-H (Digital Video Broadcasting—Handheld)and ISDB-T (Integrated Services Digital Broadcasting—Terrestrial)).

The bit stream that is to be transmitted is split into several parallelbit streams, typically hundreds or thousands. The available frequencyspectrum is split into several channels and each low bit rate stream istransmitted over one channel using some sort of known modulation schemee.g. QAM (Quadrature Amplitude Modulation) or PSK (Phase Shift Keying).The channel frequencies are chosen such that the modulated data streamsare orthogonal to each other. This means that each channel can bedeciphered independently at the receiver, since cross-talk between thesub-channels is eliminated.

In practice, each of the sub-channels may be distorted by thetransmission channel such that the amplitude and phase of eachsub-carrier must be equalised in the receiver to give good performanceusing coherent demodulation. The receiver needs a good estimate of thetransmission channel in order to carry out equalisation. In order todeal with this in the digital TV systems mentioned above, scatteredpilots are inserted at regular intervals across the frequency span ofeach symbol.

Each pilot is a symbol transmitted with known amplitude and phase andthe pilots are used for channel estimation in the receiver. In theparticular transmission schemes discussed above, every 12th sub-carrier(in the frequency direction) of each symbol is a pilot.

In order to increase the effective sampling frequency of the channel (inthe frequency direction), in the digital TV systems mentioned above, thepilot sampling grid is advanced by three sub-carriers on everyconsecutive symbol in time. This leads to a pilot sampling grid in thetime-frequency plane as shown in FIG. 1.

In FIG. 1, time (i.e. symbol number n) is shown on the y-axis. Theoldest symbol is at the top of the plot (symbol number 0) and the mostrecently received symbol is at the bottom of the plot (symbol number15). Frequency (i.e. sub-carrier k) is shown on the x-axis. Typically,there will be many more sub-carriers per symbol than are shown inFIG. 1. As indicated by the key of FIG. 1, each sub-carrier is shown bya dot and the scattered pilot sub-carriers are shown by a dot overlaidwith a rectangle.

Note, in FIG. 1, that some sub-carriers, such as sub-carrier index k=0,are designated continual pilots and as such are transmitted as a knownpilot for every symbol n.

Channel estimation at the receiver usually uses the scattered pilots. Inthe process, the receiver aims to form an estimate of the distortionapplied by the channel for each sub-carrier of each symbol received.This may be done either by interpolating (upsampling) the scatteredpilots by a factor 4 in the frequency direction. This will give a lineof virtual pilots at every third sub-carrier in the frequency direction.These resulting virtual pilots can be interpolated by a factor 3 in thefrequency direction to give a sample of the channel response for everysub-carrier. Alternatively, the interpolation may be done byinterpolating the scattered pilots by a factor 4 in the time direction.This will also give a line of virtual pilots at every third sub-carrierin the frequency direction. These resulting virtual pilots can beinterpolated by a factor 3 in the frequency direction to give a sampleof the channel response for every sub-carrier

Of course, this principle also applies for different spacings of thescattered pilots. If the spacing between pilots in each symbol is asub-carriers (in the case above, a=12) and adjacent symbol pilots areshifted by b sub-carriers (in the case above b=3), the firstinterpolation, in the time or frequency domain, will be by a factor ofa/b and the second interpolation, in the frequency domain, will be by afactor b.

Because this relates to mobile technology, we consider a fading channeli.e. one in which the receiver is moving through the interferencepattern of the transmitter. The superposition of the Doppler-shiftedcarrier wave leads to a fluctuation of the carrier amplitude and phase.This means that the received signal is amplitude and phase modulated bythe channel. Whether the first stage of the interpolation is carried outin the frequency direction or in the time direction will depend on themagnitude of the delay spread and on the magnitude of the Dopplerfrequency. The requirement to interpolate the scattered pilots by afactor 4 (in either domain) places an upper limit on the maximumtolerable delay spread.

If the delay spread falls outside

${{- \frac{T_{u}}{24}}\mspace{14mu} {to}\mspace{14mu} \frac{T_{u}}{24}},$

where T_(u) is the useful symbol duration, the interpolation in thefrequency axis will cause aliasing and, as a result, the channelestimation will be inaccurate. Thus, interpolation in the frequencydirection is only applied when the delay spread falls within the range

${- \frac{T_{u}}{24}}\mspace{14mu} {to}\mspace{14mu} {\frac{T_{u}}{24}.}$

When the delay spread falls outside the range

${{- \frac{T_{u}}{24}}\mspace{14mu} {to}\mspace{14mu} \frac{T_{u}}{24}},$

it is necessary to interpolate in the time direction.

Similarly, if the Doppler frequency exceeds

$\frac{1}{8T_{S}},$

where T_(S) is the total symbol duration, then interpolation in the timeaxis will cause aliasing and, as a result, the channel estimation willbe inaccurate.

Whether to interpolate at the first stage in the time domain or in thefrequency domain will depend on a number of factors including the delayspread and/or the Doppler frequency. Essentially, the higher the Dopplerfrequency, the more inaccurate will be the interpolation in the timeaxis and the higher the delay spread, the more inaccurate will be theinterpolation in the frequency axis.

With the presence of additive noise on the received signal, theperformance of the receiver can be improved by filtering the pilots toremove the noise.

FIG. 2 shows a set of pilot tones that may be used to perform filteringin the frequency axis for the purposes of reducing noise, and FIG. 3shows a set of pilot tones that may be used to perform filtering in thetime axis. In each figure, the pilot tones used to perform filtering areshown by a dot overlaid with a shaded rectangle. If the noise on thepilots occupies the Nyquist bandwidth f_(Ny) and the noise on thefiltered pilots occupies an effective noise bandwidth BW, then the noisepower is reduced by:

$10\; {\log_{10}\left( \frac{BW}{f_{Ny}} \right)}\mspace{11mu} {dB}$

The noise may be reduced further by performing interpolation by four inthe time axis before performing noise reduction filtering in thefrequency axis, or by performing interpolation by four in the frequencyaxis before performing noise reduction filtering in the time axis. Oneparticularly good arrangement of the prior art (as long as the Dopplerfrequency is not too high) is to perform interpolation by four in thetime axis, to perform noise reduction filtering in the frequency axisand then to interpolate by 3 in the frequency axis. The noise on thevirtual pilots generated by the interpolation in one axis occupies theNyquist bandwidth which is now 4f_(Ny), (because of the interpolation bya factor 4) so if the virtual pilots are filtering to an effective noisebandwidth BW, then the noise power is reduced by:

$10\; {\log_{10}\left( \frac{BW}{4f_{Ny}} \right)}\mspace{11mu} {dB}$

Like in FIG. 1, in FIGS. 2 and 3, time is shown on the y-axis andfrequency is shown on the x-axis. In FIG. 2, those sub-carriers overlaidwith a shaded rectangle are the inputs to an m-tap filter in thefrequency direction (here m=6). Similarly, in FIG. 3, those sub-carriersoverlaid with a shaded rectangle are the inputs to an m-tap filter inthe frequency direction (here m=6). A generic filter for the procedureis shown schematically in FIG. 4. In FIG. 4, the filter coefficients aredefined as h₀ to h_(m-1). For reducing Gaussian noise, the filter ismost likely a low-pass filter. In general, the larger m, the better thefilter performance but the more memory is required.

In a practical receiver, the cost of implementing the filters describedabove, must be considered. In general, the cost of implementing a filteralong the frequency axis is lower than the cost of implementing a filteralong the time axis. This is because the set of data points required forfiltering in the frequency direction are all present in the memory aftera symbol has been Fast Fourier Transform-ed (FFT'd) from the time domainto the frequency domain. So, no extra memory space is required in orderfor the filtering to be performed. In contrast, to apply a filter in thetime axis, pilot data from historical symbols must be stored to providethe set of data points required for filtering, and symbol data must alsobe stored to balance the delay in pilot processing to ensure thatsymbols for demodulation are time-aligned with the filtered pilots usedto equalise the received data. Or putting it another way, the FIG. 3inputs to the m-tap filter are spread out over time so must be bufferedbefore the filter output can be obtained. But the FIG. 2 filter inputsare all contained on a single symbol.

The cost of implementing a system that interpolates by four in thefrequency axis and then performs noise reduction filtering in the timeaxis will be very high because either the interpolated virtual pilotsmust be stored for a number of symbols (for example 16 symbols as shownin FIG. 3), or the virtual pilots must be calculated for a number ofsymbols (for example 16 symbols as shown in FIG. 3) when the noisereduction filtering for one symbol is performed.

The cost of implementing a system that interpolates by four in the timeaxis and then performs noise reduction filtering in the frequency axiswill be rather lower because it is only necessary to calculate and storethose virtual pilots that appear in the symbol that is beingdemodulated. This approach is advantageous in implementation cost, butit cannot work well if the Doppler frequency is so high that timeinterpolation is inaccurate.

The instantaneous channel impulse response can be estimated and used toderived a Wiener filter for frequency axis filtering. The Dopplerspectrum can also be estimated allowing a Wiener filter to beconstructed for time axis filtering. However, apart from the difficultyof estimating these parameters, there are other constraints on themaximum order of these filters and hence the amount of noise attenuationthat can be achieved.

Firstly, for frequency axis filtering, the maximum order (m) of thefrequency axis filter is constrained by the number of sub-carriers k inthe symbol and the difficulty associated at the symbols' upper and lowerfrequencies (where no further pilot sub-carriers exist). High orderfrequency axis filters are also detrimental when narrow-band interferersare present. The filtering operation causes the interference to bespread across frequency into otherwise unaffected adjacent sub-carriersi.e. the filtering actually increases the amount of interferencepresent.

Secondly, as already suggested, for time axis filtering, the maximumorder of the time-axis filter is constrained primarily by the memoryavailable in the receiver to buffer symbols and implement a causalfilter. More memory allows a higher order filter (higher m), but iscostly in terms of die area, power consumption and latency.

Some prior art systems filter in the time axis and then filter in thefrequency axis, or vice-versa, but this requires a large amount ofmemory space and processing time.

It is an object of the invention to provide a method and apparatus whichavoids or mitigates the problems of known systems described above.

SUMMARY OF THE INVENTION

According to a first aspect of the invention, there is provided a methodfor filtering a received OFDM (Orthogonal Frequency DivisionMultiplexed) signal to reduce noise, the OFDM signal comprising aplurality of symbols n in the time direction, each symbol comprising aplurality of sub-carriers k in the frequency direction, each a-thsub-carrier of each symbol being transmitted as a pilot sub-carrier withknown amplitude and phase, and each symbol having its pilot sub-carriersspaced by b sub-carriers relative to the adjacent symbol, the methodcomprising the step of: producing a filtered version of a selected pilotsub-carrier to be used in subsequent interpolation, by inputting intorespective taps of an m-tap filter, m pilot sub-carriers surrounding theselected pilot sub-carrier, the m pilot sub-carriers each satisfying arelationship between n and k, the relationship defining a diagonal linein the n-k plane.

Because the relationship defines a diagonal in the n-k plane, thefiltering spans both the frequency and time domain. This has been foundto produce improved results, for less memory space. Each pilotsub-carrier entered into the m-tap filter satisfies the n-krelationship. Because that relationship defines a diagonal in the n-kplane, the m pilot sub-carriers “surround” the selected pilotsub-carrier along that diagonal line. Preferably, the pilot sub-carrierssurround the selected pilot sub-carrier symmetrically i.e. with the samenumber of pilots either side of the selected pilot.

The method may further comprise the steps of: repeating the step ofproducing a filtered version of a selected pilot sub-carrier for aplurality of pilot sub-carriers; and interpolating the OFDM signal usingthe plurality of the filtered selected pilot sub-carriers.

By performing the interpolation after the noise has been reduced, theresulting interpolation will be more accurate. The interpolation may beused in a receiver for channel estimation, so a more accurateinterpolation will increase accuracy of the channel estimation and henceincrease accuracy of the recovered transmitted signal.

The step of interpolating may further use at least one unfiltered pilotsub-carrier. Ideally, all the pilot sub-carriers would be able to befiltered. However, for the pilot sub-carriers at the edges of the n-kplane, there are not sufficient surrounding pilot sub-carriers to beused as sensible filter inputs. Thus, the interpolation may use somefiltered pilot sub-carriers (near the centre of the n-k plane) and someunfiltered pilot sub-carriers (near the edges of the n-k plane).

In one embodiment, the step of interpolating comprises interpolating bya factor a/b in the frequency direction. This interpolation will producea set of sub-carriers at every b-th sub-carrier over every symbol i.e.parallel lines in the time direction (spaced apart by b sub-carriers inthe frequency direction). In that embodiment, the step of interpolatingmay further comprise interpolating by a factor b in the frequencydirection after interpolating by a factor a/b in the frequencydirection. This interpolation will produce the entire set ofsub-carriers in the n-k plane.

In an alternative embodiment, the step of interpolating comprisesinterpolating by a factor a/b in the time direction. This interpolationwill produce a set of sub-carriers at every b-th sub-carrier over everysymbol i.e. parallel lines in the time direction (spaced apart by bsub-carriers in the frequency direction). In that embodiment, the stepof interpolating may further comprise interpolating by a factor b in thefrequency direction after interpolating by a factor a/b in the timedirection. This interpolation will produce the entire set ofsub-carriers in the n-k plane.

Interpolating after filtering has been described above. However, it ispossible to partially or fully interpolate before filtering althoughmany such schemes are inefficient.

Thus, the method may further comprise the steps of: interpolating theOFDM signal before the filtering, using the plurality of pilotsub-carriers; repeating the step of producing a filtered version of aselected pilot sub-carrier for a plurality of pilot sub-carriers; andinterpolating, after the filtering, using the plurality of the filteredselected pilot sub-carriers.

Preferably, the step of interpolating before the filtering comprisesinterpolating by a factor a/b in the time direction. Alternatively, thestep of interpolating before the filtering may comprise interpolating bya factor a/b in the frequency direction.

Preferably, the step of interpolating after the filtering comprisesinterpolating by a factor b in the frequency direction.

Or the method may further comprise the steps of: interpolating the OFDMsignal before the filtering, using the plurality of pilot sub-carriers;and repeating the step of producing a filtered version of the a selectedpilot sub-carrier for a plurality of pilot sub-carriers.

However, in a preferred embodiment the step of interpolating comprisesinterpolating (after the filtering) by a factor 12 in the frequencydirection. This is particularly advantageous since no extra memorybuffering is required and the diagonal filtering can be performed by afilter having a large number of taps.

In another favoured embodiment, the step of interpolating comprisesinterpolating (after the filtering) by a factor 4 in the time directionthen interpolating by a factor 3 in the frequency direction.

Preferably, the step of interpolating is performed by a multi-ratepolyphase filter.

Preferably, the relationship between n and k defines a diagonal in then-k plane which has the highest ratio of pilot sub-carriers to non-pilotsub-carriers of any diagonal. In that case, the sampling rate will bethe highest effective sampling rate of any diagonal and the filteringwill be the most accurate.

In one embodiment, the relationship between n and k is given by:

k−b.n=aD,

where D is an integer.

In one embodiment, a=12 and b=3. These values are those used in thestandard TV systems, DVB-T, DVB-H and ISDB-T.

The number of taps m on the filter may be any number, but the larger thenumber of taps, the better the performance but the larger the memoryrequired for the system. Preferred embodiments of the invention use foursix or eight taps for interpolation by four in the time axis, sixteentaps for interpolation by four in the frequency axis, fifteen taps fornoise reduction filtering in the frequency axis and fifteen taps fornoise reduction filtering in the diagonal axis.

Preferably, the step of producing a filtered version of a selected pilotsub-carrier is performed by a Wiener filter which is matched to therelative levels of signal and noise in the pilot sub-carriers. In manycases a Wiener filter may be approximated by a low-pass filter.

According to a second aspect of the invention, there is provided acomputer program which, when run on computer means, causes the computermeans to carry out the method of the first aspect of the invention.

According to the second aspect of the invention, there is also provideda record carrier having stored thereon a computer program according tothe second aspect of the invention.

According to the second aspect of the invention, there is also provideda computer program which, when run on computing means for filtering areceived OFDM (Orthogonal Frequency Division Multiplexed) signal toreduce noise, the OFDM signal comprising a plurality of symbols n in thetime direction, each symbol comprising a plurality of sub-carriers k inthe frequency direction, each a-th sub-carrier of each symbol beingtransmitted as a pilot sub-carrier with known amplitude and phase, andeach symbol having its pilot sub-carriers spaced by b sub-carriersrelative to the adjacent symbol, causes the computer means to carry outthe steps of: a) filtering a selected pilot sub-carrier, by inputtinginto respective taps of an m-tap filter, m pilot sub-carrierssurrounding the selected pilot sub-carrier, the m pilot sub-carrierseach satisfying a relationship between n and k, the relationshipdefining a diagonal line in the n-k plane; b)repeating step a) for aplurality of pilot sub-carriers; and c)interpolating, in the timedimension or in the frequency dimension, using the plurality of filteredselected pilot sub-carriers from step b).

According to a third aspect of the invention, there is providedapparatus for filtering an OFDM (Orthogonal Frequency DivisionMultiplexed) signal to reduce noise, the OFDM signal comprising aplurality of symbols n in the time direction, each symbol comprising aplurality of sub-carriers k in the frequency direction, each a-thsub-carrier of each symbol being transmitted as a pilot sub-carrier withknown amplitude and phase, and each symbol having its pilot sub-carriersspaced by b sub-carriers relative to the adjacent symbol, the apparatuscomprising: an m-tap filter for filtering a selected pilot sub-carrierto be used in subsequent interpolation, the filter being arranged toreceive m pilot sub-carriers, into the respective m taps, surroundingthe selected pilot sub-carrier, the m pilot sub-carriers each satisfyinga relationship between n and k, the relationship defining a diagonalline in the n-k plane.

The apparatus may further comprise a plurality of m-tap filters forproducing filtered versions of a plurality of selected pilotsub-carriers. The resulting filter will produce a set of filtered pilotsub-carriers which can be used together for more accurate subsequentinterpolation.

Preferably, the apparatus further comprises an interpolator forinterpolating the OFDM signal using the plurality of filtered selectedpilot sub-carriers.

The interpolator may use at least one unfiltered pilot sub-carrier.Ideally, all the pilot sub-carriers would be able to be filtered.However, for the pilot sub-carriers at the edges of the n-k plane, thereare not sufficient surrounding pilot sub-carriers to be used as sensiblefilter inputs. Thus, the interpolation may use some filtered pilotsub-carriers as well as some unfiltered pilot sub-carriers.

In one embodiment, the interpolator is arranged to interpolate by afactor a/b in the frequency direction. Such an interpolator will producea set of sub-carriers at every b-th sub-carrier over every symbol i.e.parallel lines in the time direction (spaced apart by b sub-carriers inthe frequency direction). In that embodiment, the interpolator may befurther arranged to interpolate by a factor b in the frequency directionafter interpolating by a factor a/b in the frequency direction. Thissubsequent interpolation will produce the entire set of sub-carriers inthe n-k plane.

In an alternative embodiment, the interpolator is arranged tointerpolate by a factor a/b in the time direction. Such an interpolatorwill produce a set of sub-carriers at every b-th sub-carrier over everysymbol i.e. parallel lines in the time direction (spaced apart by bsub-carriers in the frequency direction). In that embodiment, theinterpolator may be further arranged to interpolate by a factor b in thefrequency direction after interpolating by a factor a/b in the timedirection. This subsequent interpolation will produce the entire set ofsub-carriers in the n-k plane.

The apparatus described above in relation to the third aspect of theinvention, has been described as a filter followed by an interpolatorwhich may interpolate in the frequency dimension followed by thefrequency dimension or in the time dimension followed by the frequencydimension, to produce a full set of sub-carriers for channel estimation.Such an interpolator may be implemented as a single interpolator or twoor more separate interpolators.

Alternatively, however, some or all the interpolating can be done beforethe filtering. Thus, the apparatus may comprise a first interpolator forinterpolating the OFDM signal before filtering, a plurality of m-tapfilters for producing filtered versions of a plurality of selected pilotsub-carriers, and a second interpolator for interpolating the OFDMsignal using the plurality of filtered selected pilot sub-carriers. Or,the apparatus may comprises an interpolator for interpolating the OFDMsignal before filtering and a plurality of m-tap filters for producingfiltered versions of a plurality of selected pilot sub-carriers.

In a preferred arrangement, however, the apparatus comprises aninterpolator arranged to interpolate (after the filtering) by a factor12 in the frequency direction. In another favoured embodiment, theapparatus comprises an interpolator arranged to interpolate (after thefiltering) by a factor 4 in the time direction and then by a factor 3 inthe frequency direction.

Preferably, the interpolator is a multi-rate polyphase filter.

Preferably, the relationship between n and k defines a diagonal in then-k plane which has the highest ratio of pilot sub-carriers to non-pilotsub-carriers of any diagonal.

In one embodiment, the relationship between n and k is given by:

k−b.n=aD,

where D is an integer.

Preferably, a=12 and b=3. These values are those used in the standard TVsystems, DVB-T, DVB-H and ISDB-T.

The number of taps m on the filter may be any number, but the larger thenumber of taps, the better the performance but the larger the memoryrequired for the system. Preferred embodiments of the invention usefifteen taps on the diagonal filter for a system arranged to use fourtaps on a time interpolation filter, or in general 4.n−1 taps on thediagonal filter for a system arranged to use n taps on a timeinterpolation filter.

Preferably, the filter comprises a Wiener filter which is matched to therelative levels of signal and noise in the pilot sub-carriers. TheWiener filter may be approximated by a low-pass filter.

The apparatus may be a receiver for OFDM signals. The receiver for OFDMsignals may be a mobile television receiver.

According to the third aspect of the invention, there is also provided areceiver for receiving an OFDM (Orthogonal Frequency DivisionMultiplexed) signal, the OFDM signal comprising a plurality of symbols nin the time direction, each symbol comprising a plurality ofsub-carriers k in the frequency direction, each a-th sub-carrier of eachsymbol being transmitted as a pilot sub-carrier with known amplitude andphase, and each symbol having its pilot sub-carriers spaced by bsub-carriers relative to the adjacent symbol, the apparatus comprising:a plurality of m-tap filters to produce filtered versions of a pluralityof selected pilot sub-carriers, each filter being arranged to receive mpilot sub-carriers, into the respective m taps, surrounding the selectedpilot sub-carrier, the m pilot sub-carriers each satisfying arelationship between n and k, the relationship defining a diagonal linein the n-k plane; an interpolator for interpolating the OFDM signalusing the plurality of filtered selected pilot sub-carriers; and ademodulator for deriving the originally transmitted signal from theinterpolated sub-carriers.

Aspects described in relation to one aspect of the invention may also beapplicable to another aspect of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

Existing systems have already been described with reference to FIGS. 1to 4, of which:

FIG. 1 is a 2D frequency-time plot showing scattered pilot sub-carriersfor a number of digital TV OFDM transmission systems;

FIG. 2 is a 2D frequency-time plot showing filtering of the scatteredpilots in the frequency direction;

FIG. 3 is a 2D frequency-time plot showing filtering of the scatteredpilots in the time direction; and

FIG. 4 is a schematic diagram of an m-tap filter.

An embodiment of the invention will now be described with reference tothe remaining figures, of which:

FIG. 5 is a 2D frequency-time plot showing filtering of the scatteredpilots according to an embodiment of the invention;

FIG. 6 is a 2D frequency-time plot showing filtering of the scatteredpilots before a frequency interpolation;

FIG. 7 is a diagram of the apparatus used for the filtering andinterpolation shown in FIG. 6;

FIG. 8 is a 2D frequency-time plot showing filtering of the scatteredpilots before a time interpolation; and

FIG. 9 is a diagram of the apparatus used for the filtering andinterpolation shown in FIG. 8.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT

FIG. 5 is a frequency time plot showing filtering performed by thefilter along the pilot diagonals according to an embodiment of theinvention. This is filtering in a domain which spans both the time andfrequency directions.

This diagonal filtering enables the reduction of noise on the estimatedchannel response in certain channel conditions using less memory thanalternative techniques. When the channel delay spread lies within therange

${{- \frac{T_{u}}{24}}\mspace{14mu} {to}\mspace{14mu} \frac{T_{u}}{24}},$

so that interpolation of the scattered pilots in the frequency directioncan be performed as the first stage of interpolation, the diagonalfiltering gives excellent results for a low implementation cost. On theother hand, when the channel delay spread lies outside

${{- \frac{T_{u}}{24}}\mspace{14mu} {to}\mspace{14mu} \frac{T_{u}}{24}},$

so that interpolation of the scattered pilots must be performed in thetime direction as the first stage of interpolation, the diagonalfiltering also gives excellent results for a low implementation cost.

A general description of the diagonal filtering follows. In thefrequency axis pilot filtering of FIG. 2, the inputs to the m-tap filterof FIG. 4 were the pilot sub-carriers for a number of sub-carriers for aparticular symbol. That is, the pilot sub-carriers to be input into thefilter are selected by fixing the symbol number and varying thesub-carrier number. (In the FIG. 2 example, k=12D and there were sixpilot sub-carriers carriers in symbol index 12 i.e. p_(12,0), p_(12,12),p_(12,24), p_(12,36), p_(12,48) and p_(12,60).)

In contrast, in the time axis pilot filtering of FIG. 3, the inputs tothe m-tap filter of FIG. 4 were the pilot sub-carriers at a particularsub-carrier over a number of symbols. That is, the pilot sub-carriers tobe input into the filter are selected by fixing the sub-carrier numberand varying the symbol number. (In the FIG. 3 example, n=4D and therewere six pilot sub-carriers in sub-carrier index 33 i.e. p_(3,33),p_(7,33), p_(11,33), p_(15,33), p_(19,33) and p_(23,33).)

In the diagonal filtering according to an embodiment of the invention,the pilot sub-carriers for inputting into the filter are selected byneither fixing the symbol number nor the sub-carrier number, but bydefining a relationship between the two. Such a relationship will definea diagonal in the sub-carrier/symbol plane. Pilot sub-carriers whichsatisfy that relationship are used as inputs into the filter.

The scattered pilot sub-carriers in FIG. 1 correspond to thosesub-carriers for which k and n satisfy:

k−3.n=12D   (1)

Each diagonal line of scattered pilots (like the one shown in FIG. 5)takes a different value of D.

Note that the following example uses the relationship given in Equation(1). However, the sub-carrier spacing of the pilots in each symbol doesnot need to be 12 (although this is what is used in the TV standardsDVB-T, DVB-H and ISBD-T). Also, the pilot shift between adjacent symbolsdoes not need to be 3 (although, again, this is what is used in DVB-T,DVB-H and ISBD-T) . In general, for a pilot sub-carrier spacing acrosseach symbol of a and a shift between adjacent symbols of b, Equation (1)becomes:

k−b.n=aD

Also note that the diagonal filtering does not need to be performed inthe particular diagonals shown in FIG. 5 (although these are found to beparticularly advantageous, as will be discussed in more detail below).The filtering could be performed in any diagonal lines (i.e. whereneither the sub-carrier index k nor the symbol index n are constant).All that is required is for a particular relationship between n and k tobe defined and the filter inputs to be the pilot sub-carriers whichsatisfy that relationship.

The mathematical analysis of the signal will now be considered.

An OFDM signal can be described in the frequency domain as a set ofsub-carriers, each of which is independently modulated by a complexvalue. (It is those complex values that are estimated in the receiver inorder to demodulate successfully.) The complex value transmitted onsub-carrier k of symbol n is designated as X_(n,k) and the complex valuereceived on sub-carrier k of symbol n is designated as Y_(n,k).

As discussed above, the scattered pilots shown in FIG. 1 correspond tothose sub-carriers for which k and n satisfy:

k−3.n=12D   (1)

The fading radio channel may be represented in the time domain as:

$\begin{matrix}{{y(t)} = {\sum\limits_{m}{\sum\limits_{l}{{x\left( {t - \tau_{m}} \right)} \cdot a_{m} \cdot {\exp \left( {{{j2\pi}\; {f_{m,l}\left( {t - \tau_{m}} \right)}} + \varphi_{m,l}} \right)}}}}} & (2)\end{matrix}$

where x(t) is the undistorted transmitted signal,

═_(m) defines the amplitude of tap m in the multi-tap channel model,

τ_(m) defines the delay of tap m, and

f_(m,l) and φ_(m,l) define the frequency and phase of one component ofthe complex fading spectrum.

Equation (2) makes use of the Jakes Doppler spectrum (i.e. effectivelyassigns a Doppler spectrum defined by f_(m,l) and to each of the m tapsbecause the channel is a fading channel) and 1 is the index of the JakesDoppler spectrum components (so the summation over 1 takes account ofthe Doppler shift for each tap).

The fading channel of Equation (2) can be expressed in the frequencydomain by applying a Fast Fourier Transform (FFT) to the signal y(t).This gives

$\begin{matrix}{Y_{n,k} = {\sum\limits_{t = 0}^{{({N - 1})}T}{{y\left( {{nT}_{S} + t} \right)}{\exp \left( {{- {j2\pi}}\; {{kt}/{NT}}} \right)}}}} & (3)\end{matrix}$

where n is the symbol number,

T is the duration of one sample, and

T_(S) is the duration of a symbol.

From Equation (2):

$\begin{matrix}{{y\left( {{nT}_{S} + t} \right)} = {\sum\limits_{m}{\sum\limits_{l}{{x\left( {{nT}_{S} + t - \tau_{m}} \right)}a_{m}{\exp \left( {{{j2\pi}\; {f_{m,l}\left( {{nT}_{S} + t - \tau_{m}} \right)}} + \varphi_{m,l}} \right)}}}}} & \;\end{matrix}$

so that Equation (3) becomes:

$\begin{matrix}{Y_{n,k} = {\sum\limits_{t = 0}^{{({N - 1})}T}{\sum\limits_{m}{\sum\limits_{l}{{x\left( {{nT}_{S} + t - \tau_{m}} \right)} \cdot a_{m} \cdot {\exp \left( {{{j2\pi}\; {f_{m,l}\left( {{nT}_{S} + t - \tau_{m}} \right)}} + \varphi_{m,l}} \right)} \cdot {\exp \left( {{- {j2\pi}}\; {{kt}/{NT}}} \right)}}}}}} & (4)\end{matrix}$

Equation (4) is an entirely accurate description of the signal and theportion exp(j2πf_(m,l)(nT_(S)+t−τ_(m))+φ_(m,l)) of Equation (4)describes the time-varying channel. If we make an approximation andreplace nT_(S)+t−τ_(m) with nT_(S)−τ_(m)=t′ i.e. set t=0 (discussedbelow), we have from Equation (4):

$Y_{n,k} = {\sum\limits_{t = 0}^{{({N - 1})}T}{\sum\limits_{m}{\sum\limits_{l}{{x\left( {{nT}_{S} + t - \tau_{m}} \right)} \cdot a_{m} \cdot {\exp \left( {{{j2\pi}\; f_{m,l}t^{\prime}} + \varphi_{m,l}} \right)} \cdot {\exp \left( {{- {j2\pi}}\; {{kt}/{NT}}} \right)}}}}}$

The portion

$\sum\limits_{t = 0}^{{({N - 1})}T}{{x\left( {{nT}_{S} + t - \tau_{m}} \right)} \cdot {\exp \left( {{- {j2\pi}}\; {{kt}/{NT}}} \right)}}$

is just the FFT×d x i.e. X_(n,k), multiplied by exp(−τ_(m)j2πk/NT), sowe have:

$Y_{n,k} = {\sum\limits_{m}{\sum\limits_{l}{X_{n,k}{{\exp \left( {{- \tau_{m}}{j2\pi}\; {k/{NT}}} \right)} \cdot a_{m} \cdot {\exp \left( {{{j2\pi}\; f_{m,l}t^{\prime}} + \varphi_{m,l}} \right)}}}}}$

which gives us:

$\begin{matrix}{Y_{n,k} = {X_{n,k}{\sum\limits_{m}{\sum\limits_{l}{a_{m} \cdot {\exp \left( {{{j2\pi}\left( {{f_{m,l}t^{\prime}} - \frac{\tau_{m}k}{NT}} \right)} + \varphi_{m,l}} \right)}}}}}} & (5)\end{matrix}$

Changing nT_(S)+t−τ_(m) to nT_(S)τ_(m)=t′ fixes the phase of each tap ofthe fading channel for the duration of each symbol. Because the phase isfixed for the duration of a symbol, Equation (5) does not describe theinter-carrier interference (ICI) that is generated by the fadingchannel. However, this simplification is valid, since diagonal filteringprovides an improvement in demodulation performance whether the ICI ispresent or not. We can therefore use Equation (5) as a reference fordescribing the operation of diagonal filtering.

Thus, Equation (5) describes a received signal Y_(n,k) that is thetransmitted signal X_(n,k) modulated by a set of time-frequencycomponents

${\exp \left( {{{j2\pi}\left( {{f_{m,l}t^{\prime}} - \frac{\tau_{m}k}{NT}} \right)} + \varphi_{m,l}} \right)}.$

When the received pilot sub-carriers are filtered to attenuate noise, itis important that the filter passes all of the time/frequency componentswith fidelity sufficient to give good demodulation performance. If thelevel of noise and the spectrum of time/frequency components is known, aWiener filter can be designed to give the best possible signal-to-noiseratio(SNR) at the filter output.

If the set of wanted time/frequency components are evenly distributedover a defined range of frequencies, then the noise attenuation achievedby a Wiener filter is given by:

$\begin{matrix}{{atten} = {{- 10}\; {\log_{10}\left( \frac{{BW}_{d}}{f_{Ny}} \right)}\mspace{11mu} {dB}}} & (6)\end{matrix}$

where BW_(d) is the desired signal bandwidth and f_(Ny) is the Nyquistfrequency for the sampled data set.

From Equation (5), the phase Θ of each time/frequency component of thefading channel such that

$\begin{matrix}{{\exp \left( {{{j2\pi}\left( {{f_{m,l}t^{\prime}} - \frac{\tau_{m}k}{NT}} \right)} + \varphi_{m,l}} \right)} = {\exp ({j\Theta})}} & (7) \\{{is}\mspace{14mu} {given}\mspace{14mu} {by}\text{:}} & \; \\{\Theta_{n,k,m,l} = {{2{\pi \left( {{f_{m,l}\left( {{nT}_{S} - \tau_{m}} \right)} - \frac{\tau_{m}k}{NT}} \right)}} + \varphi_{m,l}}} & \;\end{matrix}$

The ratio

$\frac{B\; W_{d}}{f_{Ny}}$

from Equation (6) is equal to

$\frac{1}{\pi}$

multiplied by the maximum change in phase between two successive samplesfor all values of m and 1. We will assume that the time axis componentsof Equation (7) are evenly distributed across a range such that−τ_(max)≦τ_(m)≦τ_(max). We further assume that the frequency axiscomponents of Equation (7) are evenly distributed across a range suchthat −f_(max)≦f_(m,l)≦f_(max).

Given these assumptions, we can calculate the noise attenuation for thethree cases of 1) filtering in the frequency direction (prior art), 2)filtering in the time direction (prior art) and 3) diagonal filtering(the invention). We can then compare them.

1) For frequency axis filtering where k=12D:

In equation (7), we set n=1 and k=12 to give:

$\Theta_{1,12,m,l} = {{2{\pi \left( {{f_{m,l}\left( {T_{S} - \tau_{m}} \right)} - \frac{\tau_{m}12}{N\; T}} \right)}} + \varphi_{m,l}}$

and we set n=1 and k=24 to give:

$\Theta_{1,24,m,l} = {{2{\pi \left( {{f_{m,l}\left( {T_{S} - \tau_{m}} \right)} - \frac{\tau_{m}24}{N\; T}} \right)}} + \varphi_{m,l}}$

So, the change in phase between successive samples of tap m is

${{\Theta_{1,24,m,l} - \Theta_{1,12,m,l}}} = {{2{\pi \left( \frac{12\tau_{m}}{N\; T} \right)}} = \frac{24{\pi\tau}}{N\; T}}$

and the maximum change in phase between successive samples for all m and1 is

${\max \left( {{\Theta_{1,{24.m},l} - \Theta_{1,12,m,l}}} \right)} = \frac{24{\pi\tau}_{\max}}{N\; T}$${So},{{atten} = {- {\log_{10}\left( {\frac{1}{\pi}{\max \left( {{\Theta_{1,24,m,l} - \Theta_{1,12,m,l}}} \right)}} \right)}}}$

which gives:

For frequency axis filtering:

$\begin{matrix}{{atten} = {{- 10}{\log_{10}\left( \frac{24\tau_{\max}}{N\; T} \right)}}} & (8)\end{matrix}$

For time axis filtering where n=4D:

In equation (7), we set n=1 and k=12 to give:

$\Theta_{1,12,m,l} = {{2{\pi \left( {{f_{m,l}\left( {T_{S} - \tau_{m}} \right)} - \frac{\tau_{m}12}{N\; T}} \right)}} + \varphi_{m,l}}$

and we set n=5 and k=12 to give:

$\Theta_{5,12,m,l} = {{2{\pi \left( {{f_{m,l}\left( {{5.T_{S}} - \tau_{m}} \right)} - \frac{\tau_{m}12}{N\; T}} \right)}} + \varphi_{m,l}}$

So, the change in phase between successive samples of tap m component 1is

|Θ_(5,12,ml)−Θ_(1,12,m,l)|=8πf _(m,l) T _(S)

and the maximum change in phase between successive samples for all m and1 is

max(|Θ_(5,12,m,l)−Θ_(1,12,m,l)|)=8πf _(max) T _(S)

So, for time axis filtering: atten=−10 log₁₀(8f _(max) T _(S)) (9)

For diagonal filtering where k−3.n=12D:

In equation (7), we set n=1 and k=12 to give:

$\Theta_{1,12,m,l} = {{2{\pi \left( {{f_{m,l}\left( {T_{S} - \tau_{m}} \right)} - \frac{\tau_{m}12}{N\; T}} \right)}} + \varphi_{m,l}}$

and we set n=2 and k=15 to give:

$\Theta_{2,15,m,l} = {{2{\pi \left( {{f_{m,l}\left( {{2.T_{S}} - \tau_{m}} \right)} - \frac{\tau_{m}15}{N\; T}} \right)}} + \varphi_{m,l}}$

So, the change in phase between successive samples=

${{\Theta_{2,15,m,l} - \Theta_{1,12,m,l}}} = {{2\pi \; f_{m,l}T_{S}} - \frac{6.{\pi.\tau_{m}}}{N\; T}}$

and the maximum change in phase between successive samples for all m and1 is

${\max \left( {{\Theta_{2,15,m,l} - \Theta_{1,12,m,l}}} \right)} = {{2\pi \; f_{\max}T_{S}} + \frac{6{\pi\tau}_{\max}}{N\; T}}$

So in summary:

For frequency axis filtering:

$\begin{matrix}{{atten} = {{- 10}{\log_{10}\left( \frac{24\tau_{\max}}{N\; T} \right)}}} & (8)\end{matrix}$

For time axis filtering:

atten=−10 log₁₀(8f _(max) T _(S))   (9)

and

For diagonal filtering:

$\begin{matrix}{{atten} = {{- 10}{\log_{10}\left( {{2f_{\max}T_{S}} + \frac{6\tau_{\max}}{N\; T}} \right)}}} & (10)\end{matrix}$

From equations (8), (9) and (10), we see that the diagonal filteringtechnique of this embodiment of the present invention has much betternoise attenuation than the known time axis or frequency axis filteringtechniques.

The bandwidth of the wanted signal in the diagonal domain is a functionof both the channel impulse response and the Doppler frequency spread asseen at the receiver. The diagonal filter bandwidth can be set either asa Wiener filter matched to the instantaneous bandwidth of the signal inthe diagonal, or it can be set to match known channel conditions wherethe maximum Doppler frequency and delay spread are constrained.

As already discussed, channel estimation in the receiver can beperformed either by time axis and then frequency axis interpolation(suitable for wide delay spread) or by frequency axis interpolation(suitable for narrow delay spread).

Two specific examples of the invention will be given below. In Example1, the interpolation takes place in the frequency domain only. InExample 2, the interpolation takes place in the time domain and then inthe frequency domain.

EXAMPLE 1

A specific example of the diagonal filtering as described above will nowbe described with reference to FIGS. 6 and 7.

This example shows the application of a 15 tap noise reducing diagonalfilter to a channel estimator using frequency axis interpolation.

FIG. 6 shows a subset of the time frequency plane for 16 consecutiveOFDM symbols. As in FIGS. 1 to 4, the scattered pilots are highlightedin the diagram. In this example, the channel estimate for symbol number7 is being estimated (symbol number 0 is the most recently received).

The channel estimation is performed by interpolating by a factor 12between the scattered pilot sub-carriers (in this case sub-carriersnumbered 0, 9, 21, 33, 45 i.e. those scattered pilots falling withinsymbol 7). The result is a channel estimate for each of the sub carriersi.e. the band at symbol 7 shown by the dotted lines in FIG. 6. Thischannel estimate is usually a single complex value per sub-carrier andis used by the equalizer to correct for the distortion encountered bythe channel.

We could simply use the raw values of the pilots at 0, 9, 21, 33 and 45to perform the interpolation. But, as already mentioned, it isadvantageous to perform filtering to those scattered pilots, beforeusing them for interpolation.

According to the invention, the filtering is carried out along the pilotdiagonals i.e. in a domain spanning both time and frequency. Thisreduces the Gaussian noise on the received pilots before interpolation.

Consider the filtering applied to sub-carrier 21 of symbol 7. FIG. 5shows (in dark shading) the pilots that are input to one suchapplication of the filter (like that shown in FIG. 4 with m=15) in orderto produce a noise reduced channel estimate for sub-carrier 21 of symbol7. The diagonal filter is applied to produce a noise reduced channelestimate

{circumflex over (p)}_(7,21) =p _(14,0) h ₀ +p _(13,3) h ₁ +p _(12,6) h₂ +p _(11,9) h ₃ +p _(10,12) h ₄ +p _(9.15) h ₅ +p _(8,18) h ₆ +p_(7,21) h ₇ 30 p _(6,24) h ₈ +p _(5,27) h ₉ +p _(4,30) h ₁₀ +p _(3,33) h₁₁ +p _(2,36) h ₁₂ +p _(1,39) h ₁₃ +p _(0.42) h ₁₄   (13)

This noise reduced {circumflex over (p)}_(7,21) can be used instead ofthe noisy p_(7,21) as the input for the interpolation.

Similarly, the other scattered pilots in the symbol number 7 could befiltered. For example:

{circumflex over (p)} _(7,23) =p _(14,12) h ₀ +p _(13,13) h ₁ +p_(12,18) h ₂ +p _(11,21) h ₃ +p _(10,24) h ₄ +p _(9,27) h ₅ +p _(8,30) h₆ +p _(7,33) h ₇ +p _(6,36) h ₈ +p _(5,39) h ₉ +p _(4,42) h ₁₀ +p_(3,45) h ₁₁ +p _(2,48) h ₁₂ +p _(1,51) h ₁₃ +p _(0,54) h ₁₄

The filter would run a similar pattern across the symbol in anincreasing frequency direction until noise reduced channel estimates areavailable for all scattered pilot sub-carriers of symbol 7 with theexception of those at the symbol's upper and lower frequency boundaries.In those cases, there is insufficient pilot information to filterdiagonally, so the pilot sub-carriers are used directly rather thanafter filtering. This may be achieved by adjusting the group delay ofthe interpolator.

So, the inputs for the interpolation along the frequency direction forsymbol 7 would be p_(7,0), {circumflex over (p)}_(7,9), {circumflex over(p)}_(7,21), {circumflex over (p)}_(7,33) and {circumflex over(p)}_(7,45). This is shown in FIG. 7. The interpolator is usuallyimplemented as a multi-rate polyphase filter where the bandwidth of thefilter can be narrowed to provide some across frequency filtering.

EXAMPLE 2

A second specific example of the diagonal filtering as described abovewill now be described with reference to FIGS. 8 and 9.

This example shows the application of noise reducing diagonal filter toa channel estimator using time axis interpolation.

FIG. 8 shows a subset of the time frequency plane for 16 consecutiveOFDM symbols. As in FIGS. 1 to 5, the scattered pilots are highlightedin the diagram. In this example, the channel estimate for symbol number7 is being estimated (symbol number 0 is the most recently received).

In the absence of filtering (i.e. using the raw pilot values), thechannel estimate is formed by first interpolating between scatteredpilots in the time axis (upsampling by a factor 4) and then using thosechannel estimates to upsample in the frequency axis (upsampling by afactor 3).

The interpolation in time would produce all values at every 3rdsub-carrier including channel estimates for p_(7,0), p_(7,31), p_(7,6)and so on. In FIG. 8, the generation of p_(7,12) is highlighted, andthis uses the scattered pilots on sub-carrier 12 from other symbols bothproceeding and preceding symbol 7.

In this example, the diagonal filtering is used prior to the timeinterpolation stage to remove some broadband noise from the pilots. FIG.8 shows the application of two diagonal filters to remove noise fromchannel estimates p_(10,12) and p_(6,12). Note that p_(14,12) andp_(2,12) are not filtered in this example since, to do so, would requireadditional symbol storage and these two are less dominant contributorsof noise to the interpolation stage. With the seven filter coefficientsof the diagonal filter defined as h₀ to h₆ (i.e. m=7 in FIG. 4), thenoise reduced pilot estimates {circumflex over (p)}_(10,12) and{circumflex over (p)}_(6,12) given by:

{circumflex over (p)} _(10,12) =p _(13,3) h ₀ +p _(12,6) h ₀ +p _(11,9)h ₂ +p _(10,12) h ₃ +p _(9,15) h ₄ +p _(8,18) h ₅ +p _(7,21) h ₆

and

{circumflex over (p)} _(6,12) =p _(9,3) h ₀ +p _(8,6) h _(1+p) _(7,9) h₂ +p _(6,13) h ₄ +p _(4,18) h ₅ +p _(3,21) h ₆

When diagonal filtering is enabled, the inputs to the time interpolationstage for sub-carrier 12 are now p_(14,12), {circumflex over(p)}_(10,12), {circumflex over (p)}_(6,12) and p_(2,12). This is shownin FIG. 9.

For the diagonal filtering that precedes frequency axis filtering(Example 1), we can use 15 taps for a pilot store sized to allow 4-taptime interpolation (in general 4n−1 where n is the number of taps fortime interpolation). For the diagonal filtering that precedes time axisfiltering (Example 2) we must either increase the size of the pilotstore or we must reduce the number of taps to avoid the need for pilotsfrom symbols earlier or later than those held in the pilot store. Thisis why the number of taps in Example 2 is only 7 as compared with 15 inExample 1.

In the examples described, the diagonals are chosen to satisfy Equation(1). However, as previously mentioned, this is not necessary and thediagonals may lie in any diagonal direction on the symbol/sub-carrier(n-k) plane. However, for DVB-T and other standard TV systems, where thespacing of the pilot sub-carriers in each symbol is 12 and the pilots ineach symbol are shifted relative to the adjacent symbol by 3sub-carriers, the most effective filtering technique is the one where nand k satisfy the relationship given in Equation (1). This is becausethese diagonals have the highest effective sampling rate which gives thebest SNR after filtering.

In the examples discussed, the diagonal filtering is carried out beforeany interpolation. Indeed this is preferable but not essential.

In fact, all orders of operation are possible (though some are veryinefficient). The good orders of operation are:

1) Diagonal filtering followed by frequency interpolation by a factor 12(like Example 1). This is good when τ_(max)<24/NT.

2) Diagonal filtering followed by time interpolation by a factor 4 andfrequency interpolation by a factor 3. This is good when τ_(max)>24/NTand the Doppler frequency is not too high).

One application of the invention is for a receiver for OFDM signals. Thereceiver may be arranged to filter the received signals diagonally inaccordance with the invention in order to remove broadband noise. Then,the receiver can interpolate the sub-carriers and, from the obtainedchannel estimates, derive the transmitted OFDM signal. As alreadymentioned, OFDM transmission is used in digital TV systems (e.g. DVB-T(Digital Video Broadcasting—Terrestrial), DVB-H (Digital VideoBroadcasting—Handheld) and ISDB-T (Integrated Services DigitalBroadcasting—Terrestrial)). One particular application of the inventionis in a mobile digital TV receiver. OFDM is also used in digital audiobroadcasting (such as Eureka 147, HD Radio, T-DMB and ISDB-TSB), ADSLand VDSL broadband access and IEEE 802.11a and 802.11g Wireless LANsamongst others and the invention is applicable to any such systems whichuse OFDM signals having pilots for channel estimation.

1. A method for filtering a received OFDM (Orthogonal Frequency DivisionMultiplexed) signal to reduce noise, the OFDM signal comprising aplurality of symbols n in the time direction, each symbol comprising aplurality of sub-carriers k in the frequency direction, each a-thsub-carrier of each symbol being transmitted as a pilot sub-carrier withknown amplitude and phase, and each symbol having its pilot sub-carriersspaced by b sub-carriers relative to the adjacent symbol, the methodcomprising the step of: producing a filtered version of a selected pilotsub-carrier to be used in subsequent interpolation, by inputting intorespective taps of an m-tap filter, m pilot sub-carriers surrounding theselected pilot sub-carrier, the m pilot sub-carriers each satisfying arelationship between n and k, the relationship defining a diagonal linein the n-k plane.
 2. A method according to claim 1, further comprisingthe steps of: repeating the step of producing a filtered version of aselected pilot sub-carrier for a plurality of pilot sub-carriers; andinterpolating the OFDM signal using the plurality of the filteredselected pilot sub-carriers.
 3. A method according to claim 2, whereinthe step of interpolating further uses at least one unfiltered pilotsub-carrier.
 4. A method according to claim 2, wherein the step ofinterpolating comprises interpolating by a factor a/b in the frequencydirection.
 5. A method according to claim 4, wherein the step ofinterpolating further comprises interpolating by a factor b in thefrequency direction after interpolating by a factor a/b in the frequencydirection.
 6. A method according to claim 2, wherein the step ofinterpolating comprises interpolating by a factor a/b in the timedirection.
 7. A method according to claim 6, wherein the step ofinterpolating further comprises interpolating by a factor b in thefrequency direction after interpolating by a factor a/b in the timedirection.
 8. A method according to claim 2, wherein the step ofinterpolating is performed by a multi-rate polyphase filter.
 9. A methodaccording to claim 1, wherein the relationship between n and k defines adiagonal in the n-k plane which has the highest ratio of pilotsub-carriers to non-pilot sub-carriers of any diagonal.
 10. A methodaccording to claim 1, wherein the relationship between n and k is givenby:k−b.n=aD, where D is an integer.
 11. A method according to claim 1,wherein a=12 and b=3.
 12. A method according to claim 1, wherein thestep of producing a filtered version of a selected pilot sub-carrier isperformed by a Wiener filter matched to the relative levels of signaland noise in the pilot sub-carriers.
 13. A method according to claim 1,wherein the step of producing a filtered version of a selected pilotsub-carrier is performed by a low-pass filter.
 14. A computer programwhich, when run on computer means, causes the computer means to carryout the method of claim
 1. 15. A record carrier having stored thereon acomputer program according to claim
 14. 16. A computer program which,when run on computing means for filtering a received OFDM (OrthogonalFrequency Division Multiplexed) signal to reduce noise, the OFDM signalcomprising a plurality of symbols n in the time direction, each symbolcomprising a plurality of sub-carriers k in the frequency direction,each a-th sub-carrier of each symbol being transmitted as a pilotsub-carrier with known amplitude and phase, and each symbol having itspilot sub-carriers spaced by b sub-carriers relative to the adjacentsymbol, causes the computer means to carry out the steps of : a)filtering a selected pilot sub-carrier, by inputting into respectivetaps of an m-tap filter, m pilot sub-carriers surrounding the selectedpilot sub-carrier, the m pilot sub-carriers each satisfying arelationship between n and k, the relationship defining a diagonal linein the n-k plane; b)repeating step a) for a plurality of pilotsub-carriers; and c)interpolating, in the time dimension or in thefrequency dimension, using the plurality of filtered selected pilotsub-carriers from step b).
 17. Apparatus for filtering an OFDM(Orthogonal Frequency Division Multiplexed) signal to reduce noise, theOFDM signal comprising a plurality of symbols n in the time direction,each symbol comprising a plurality of sub-carriers k in the frequencydirection, each a-th sub-carrier of each symbol being transmitted as apilot sub-carrier with known amplitude and phase, and each symbol havingits pilot sub-carriers spaced by b sub-carriers relative to the adjacentsymbol, the apparatus comprising: an m-tap filter for filtering aselected pilot sub-carrier to be used in subsequent interpolation, thefilter being arranged to receive m pilot sub-carriers, into therespective m taps, surrounding the selected pilot sub-carrier, the mpilot sub-carriers each satisfying a relationship between n and k, therelationship defining a diagonal line in the n-k plane.
 18. Apparatusaccording to claim 17, further comprising a plurality of m-tap filtersfor producing filtered versions of a plurality of selected pilotsub-carriers.
 19. Apparatus according to claim 18, further comprising aninterpolator for interpolating the OFDM signal using the plurality offiltered selected pilot sub-carriers.
 20. Apparatus according to claim19, wherein the interpolator uses at least one unfiltered pilotsub-carrier.
 21. Apparatus according to claim 19, wherein theinterpolator is arranged to interpolate by a factor a/b in the frequencydirection.
 22. Apparatus according to claim 21, wherein the interpolatoris further arranged to interpolate by a factor b in the frequencydirection after interpolating by a factor a/b in the frequencydirection.
 23. Apparatus according to claim 19, wherein the interpolatoris arranged to interpolate by a factor a/b in the time direction. 24.Apparatus according to claim 23, wherein the interpolator is furtherarranged to interpolate by a factor b in the frequency direction afterinterpolating by a factor a/b in the time direction.
 25. Apparatusaccording to claim 19, wherein the interpolator is a multi-ratepolyphase filter.
 26. Apparatus according to claim 17, wherein therelationship between n and k defines a diagonal in the n-k plane whichhas the highest ratio of pilot sub-carriers to non-pilot sub-carriers ofany diagonal.
 27. Apparatus according to claim 17, wherein therelationship between n and k is given by:k−b.n=aD, where D is an integer.
 28. Apparatus according to claim 17,wherein a =12 and b
 3. 29. Apparatus according to claim 17, wherein thefilter comprises a Wiener filter matched to the relative levels ofsignal and noise in the pilot sub-carriers.
 30. Apparatus according toclaim 17, wherein the filter comprises a low-pass filter.
 31. Apparatusaccording to claim 17 wherein the apparatus is a receiver for OFDMsignals.
 32. Apparatus according to claim 31, wherein the receiver forOFDM signals is a mobile television receiver.
 33. A receiver forreceiving an OFDM (Orthogonal Frequency Division Multiplexed) signal,the OFDM signal comprising a plurality of symbols n in the timedirection, each symbol comprising a plurality of sub-carriers k in thefrequency direction, each a-th sub-carrier of each symbol beingtransmitted as a pilot sub-carrier with known amplitude and phase, andeach symbol having its pilot sub-carriers spaced by b sub-carriersrelative to the adjacent symbol, the apparatus comprising: a pluralityof m-tap filters to produce filtered versions of a plurality of selectedpilot sub-carriers, each filter being arranged to receive m pilotsub-carriers, into the respective m taps, surrounding the selected pilotsub-carrier, the m pilot sub-carriers each satisfying a relationshipbetween n and k, the relationship defining a diagonal line in the n-kplane; an interpolator for interpolating the OFDM signal using theplurality of filtered selected pilot sub-carriers; and a demodulator forderiving the originally transmitted signal from the interpolatedsub-carriers.